Fractal Algorithm Research Articles

Multi-alpha fractal iteration algorithm

Multi-alpha fractal iteration algorithm

An advanced cryptographic scheme for DICOM medical image encryption using a novel spatiotemporal chaotic lattice

Ensuring the privacy and security of medical imaging data is crucial. Most existing methods focus on encrypting images in common formats, neglecting the unique challenges posed by medical formats. In this paper an advanced encryption algorithm based on a multi-dimensional and multi-parametric spatiotemporal coupled chaotic lattice (Double-MsCcL) system is proposed. The Double-MsCcL system enhances the complexity of chaotic sequences, and provides a robust foundation for medical image encryption. The encryption method proposed combines double-layer random DNA diffusion and fractal random permutation. Medical information is embedded in the image pixels, serving as the cryptosystem key. The designed double-layer DNA random diffusion algorithm alters pixel values, while the fractal random permutation algorithm disrupts pixel positions. This proposed approach effectively hides sensitive information, strengthens resistance to plaintext attacks, and address the often-overlooked Uint16 format of DICOM images. Comprehensive performance evaluations have shown that the proposed encryption scheme offers significant advantages in protecting sensitive medical imaging data. Our algorithm exhibits better performance in resisting plaintext analysis, statistical, and differential attacks, demonstrating significant security compared to existing state-of-the-art methods, which can be widely applied in the field of modern medical data protection.

Damage evolution law of multi-hole blasting igneous rock and quantitative evaluation model of damage degree based on fractal theory and clustering algorithm

The geological phenomenon of igneous rock invading coal seam is widely distributed, which induces mining risk and affects efficient mining. The pre-splitting blasting method of igneous rock is feasible but difficult to implement accurately, resulting in unnecessary safety and environmental pollution risks. In this paper, the blasting model with penetrating structural plane and the multi-hole blasting model with different hole spacing were established based on the Riedel–Hiermaier–Thoma (RHT) damage constitutive to explore the stress wave propagation law under detonation. The damage cloud diagram and damage degree algorithm were used to quantitatively describe the spatio-temporal evolution of blasting damage. The results show that the explosion stress wave presents a significant reflection stretching effect under the action of the structural plane, which can effectively aggravate the presplitting blasting degree of the rock mass inside the structural plane. The damage range of rock mass is synchronously evolved with the change of blasting hole spacing. The blasting in the igneous rock intrusion area of the 21,914 working face is taken as an application example, and the damage degree of rock mass is reasonably evaluated by the box-counting dimension and K-means clustering method, which proves the effectiveness of the blasting scheme and provides reference value for the implementation of related blasting projects.

Evaluation of forest loss data using fractal algorithms: case study Eastern Carpathians–Romania

Logging causes the fragmentation of areas with direct implications for hydrological processes, landslides, or habitats. The assessment of this fragmentation process plays an important role in the planning of future logging, reconstruction, and protection measures for the whole ecosystem. The methodology used includes imaging techniques applying two fractal indices: the Fractal Fragmentation Index (FFI) and the Fractal Fragmentation and Disorder Index (FFDI). The results showed the annual evolution and disposition of deforested areas. Only 3% of deforestation resulted in the fragmentation and splitting of forest plots. The remaining 97% resulted in the reduction of existing compact stands without fragmentation. The method has many advantages in quantifying the spatial evolution of forests, estimating the capture of carbon emissions and establishing sustainability of bird and animal habitats. The analysis took place in the Eastern Carpathians, in Romania, in the time period of 2001–2022.

A REVIEW ON OPTIMAL PLACEMENT AND SIZING METHODS OF DISTRIBUTION GENERATION SOURCES

This manuscript outlines various work carried out in the field of Distributed Generation (DG). Increase in power consumption and shortage in transmission capabilities are addressed by DGs. In order to maximize the potential benefits, it is imperative to place the DGs at optimal locations and the DGs should have optimal size pertaining to that location. There are several research works that are carried out on the placement and sizing of DGs. Nonetheless, the methodical principle for this issue is still unsettled. Various optimization strategies can be used to obtain the appropriate placement and sizing of distributed generation (DG) in grids. This study provides a comprehensive overview of several DG placement approaches, including stochastic fractal search algorithms, particle swarm optimization, symbiotic search algorithms, opposition-based tuneable chaotic differential evaluation, and more. The benefits and potential uses of each method are briefly covered in this study. The study sheds light on the efforts made to determine the best location and size of DGs.

A novel grey forecasting model with generalised fractal derivative and its optimisation

PurposeThe purpose of this paper is to propose a new grey prediction model, GOFHGM (1,1), which combines generalised fractal derivative and particle swarm optimisation algorithms. The aim is to address the limitations of traditional grey prediction models in order selection and improve prediction accuracy.Design/methodology/approachThe paper introduces the concept of generalised fractal derivative and applies it to the order optimisation of grey prediction models. The particle swarm optimisation algorithm is also adopted to find the optimal combination of orders. Three cases are empirically studied to compare the performance of GOFHGM(1,1) with traditional grey prediction models.FindingsThe study finds that the GOFHGM(1,1) model outperforms traditional grey prediction models in terms of prediction accuracy. Evaluation indexes such as mean squared error (MSE) and mean absolute error (MAE) are used to evaluate the model.Research limitations/implicationsThe research study may have limitations in terms of the scope and generalisability of the findings. Further research is needed to explore the applicability of GOFHGM(1,1) in different fields and to improve the model’s performance.Originality/valueThe study contributes to the field by introducing a new grey prediction model that combines generalised fractal derivative and particle swarm optimisation algorithms. This integration enhances the accuracy and reliability of grey predictions and strengthens their applicability in various predictive applications.

Improved stochastic fractal search algorithm involving design operators for solving parameter extraction problems in real-world engineering optimization problems

The characteristic parameters of renewable energy sources (RESs) are changes over time under changing operating conditions. Therefore, the accuracy of the model is important in order to establish appropriate control and operating plans for the stable operation of such systems. Determining the parameters of RESs and creating an accurate model of them is an inevitable reality and plays an important role in the success of system modeling. Many methods have been used to determine these parameters in the literature. Furthermore, optimization algorithms are now considered to be among the most significant approaches for resolving problems pertaining to system parameter extraction in many scientific areas. In the study, this parameter extraction is done by a new optimization method called stochastic fractal search algorithm (FDB-NSM-SFS-OBLs), which includes natural survivor updating (NSM) and fitness distance balance (FDB) guiding mechanisms, and opposite based learning (OBL) methods. The performance of the proposed FDB-NSM-SFS-OBL algorithm has been tested in two different experimental studies. In the first experimental study, the proposed approach is tested on CEC2020 benchmark test functions and the algorithm structure containing the best OBL approach is determined using nonparametric Wilcoxon and Friedman statistical analysis methods. The second experimental study is carried out with the proposed optimization algorithm to estimate the parameters of the photovoltaic cell used in the modeling, which is the building block of photovoltaic panels used in renewable energy systems, proton-exchange membrane fuel cell (PEMFC) that is another renewable energy source, and Li-Ion battery used as a backup power unit. The FDB-NSM-SFS-OBL algorithm, which is used both in the CEC2020 benchmark test functions and in determining the parameters of photovoltaic (PV) cells, PEMFC and Li-Ion batteries, performed better in searching and finding the global solution point during the optimization process.

A novel fractal interpolation function algorithm for fractal dimension estimation and coastline geometry reconstruction: a case study of the coastline of Kingdom of Saudi Arabia

A novel fractal interpolation function algorithm for fractal dimension estimation and coastline geometry reconstruction: a case study of the coastline of Kingdom of Saudi Arabia

The origin, development, and application of fractal geometry theory in architecture

Fractal geometry plays a crucial role in the study of fractals, with wide-ranging applications and it is closely related to architectural design creation, notably in architecture. Fractals are becoming more prevalent in todays society and can be used to describe a variety of extremely irregular items in the actual world. This article aims to provide an overview and analysis of the significant implications of fractal geometry in architecture, exploring its relationship with elements in nature, such as trees. By searching, organizing data, and elucidating examples, the article delves into the origin and basic background of fractal geometry. The use of fractal geometry in architecture demonstrates the perfect symbiosis between fractal and nature through analysis of TOD, the ancient gardens in Suzhou, and other practical applications. One notable fractal algorithm is the L-system, a modeling approach expressing fractal concepts, enabling parameterization and architectural design. Fractal geometry successfully expands possibilities for the harmonious coexistence of architecture and nature, embodying numerous natural features and human-centric ideas.

Inspection policy optimization for hierarchical multistate systems under uncertain mission scenarios: A risk-averse perspective

Most engineered systems intend to perform missions with a pre-specified target success probability to reduce undesirable failure risks. Before executing the next mission, inspection activities are conducted across various physical levels for assessing the probability of mission success. However, due to the randomness of a system’s degradation behavior and the presence of measurement errors, inspection results inevitably contain uncertainty. Meanwhile, mission durations and acceptable system states may also be uncertain, due to uncontrollable factors, such as random operating environments and mission demands. In such a circumstance, it is of great significance to identify the optimal multilevel inspection policy to answer, as great confident as possible, the question that the system can complete the next mission with a target mission success probability. This paper develops a novel metric to gauge the effectiveness of a multilevel inspection policy to assess if the system can complete the next mission with a pre-specified target success probability from a risk-averse perspective, based on which an optimization method is proposed to seek an inspection policy under uncertain scenarios with the aim of minimizing the maximum regret of the proposed metric. A stochastic fractal search algorithm, along with two tailored local search rules, is designed to efficiently resolve the resulting optimization problem. Two cases, including a three-component system and a rocket fueling mechanism’s control system, are used to illustrate the efficacy of the proposed approach, which is capable of effectively identifying the risk of mission failures by inspection policies.

Determining mammalian cells state by fractal micromotion

We applied four fractal dimension estimation algorithms on the temporal electrical impedance signal of normal MDCK type II cell cultures monitored by ECIS technique and showed that the fractal dimension due to micromotion allows discriminating processes not sensed by the spectral impedance of the culture. In this work we subjected cell cultures to electric current damage and drug exposure to analyze the changes in the fractal structure of the temporal signal. Among the changes presented and detected are the differentiation between a healthy monolayer and one exposed to a drug, as well as the distinction between a seeding process and a wound-healing process performed by electric current. The four algorithms used were validated by applying them on topological functions of known fractal dimension, a study that determined the necessary conditions for a correct estimation.

Image Encryption Technology Based on Fractal Image Compression Algorithm

As the most commonly used information transmission method, digital images often store a large amount of personal information. To prevent information leakage, encrypting images is essential. Common image encryption techniques suffer from certain limitations, such as overly simple encryption methods and long encryption times. In response to the above issues, this study proposes the Frobenius canonical form image encryption scheme. It calculates the fractal code through the fractal compression algorithm and to encrypt the image, it adjusts the brightness coefficient in the fractal code. To address unsatisfactory correlation coefficients in encrypted images, the Frobenius canonical form image encryption is improved by introducing the Arnold transformation encryption, which combines the two methods to reduce correlation coefficients. Finally, the knight tour algorithm is put forward. In response to the long image scrambling time in the knight tour algorithm, the Tetragonal theorem is combined with the scheme to encrypt the image. It is then re-encrypted using the Frobenius canonical form. The experimental findings illustrate that when using Frobenius canonical form, Arnold transformation combined with Frobenius canonical form, and the tetragonal algorithm combined with knight tour algorithm to encrypt Lena images, the three decryption methods correspond to image similarity of over 70%, over 80%, and over 90%, respectively. Combining the tetragonal algorithm and the knight tour algorithm can significantly increase the security of image encryption.

Comprehensive Study of Compression and Texture Integration for Digital Imaging and Communications in Medicine Data Analysis

In response to the COVID-19 pandemic and its strain on healthcare resources, this study presents a comprehensive review of various techniques that can be used to integrate image compression techniques and statistical texture analysis to optimize the storage of Digital Imaging and Communications in Medicine (DICOM) files. In evaluating four predominant image compression algorithms, i.e., discrete cosine transform (DCT), discrete wavelet transform (DWT), the fractal compression algorithm (FCA), and the vector quantization algorithm (VQA), this study focuses on their ability to compress data while preserving essential texture features such as contrast, correlation, angular second moment (ASM), and inverse difference moment (IDM). A pivotal observation concerns the direction-independent Grey Level Co-occurrence Matrix (GLCM) in DICOM analysis, which reveals intriguing variations between two intermediate scans measured with texture characteristics. Performance-wise, the DCT, DWT, FCA, and VQA algorithms achieved minimum compression ratios (CRs) of 27.87, 37.91, 33.26, and 27.39, respectively, with maximum CRs at 34.48, 68.96, 60.60, and 38.74. This study also undertook a statistical analysis of distinct CT chest scans from COVID-19 patients, highlighting evolving texture patterns. Finally, this work underscores the potential of coupling image compression and texture feature quantification for monitoring changes related to human chest conditions, offering a promising avenue for efficient storage and diagnostic assessment of critical medical imaging.

A Method and Algorithm for Implementing the Mandelbrot Set for Processing Complex Structured Images

The purpose of research. In our life, fractals are ubiquitous, for example, in nature, there are a huge number of figures similar to themselves and built according to certain laws. Fractals are used in computer graphics, economics, radio engineering, physics and many other fields. The use of fractals in various fields of science can open up many new possibilities. Therefore, the development of a software product designed to visualize the Mandelbrot set is an urgent task. The purpose of the research is to develop a software product designed for processing complex structured images based on fractal methods and algorithms for visualizing the Mandelbrot set.Methods. The Java programming language was used to implement the software product in order to visualize the Mandelbrot set. The SQLite database was used as a local data store. Libraries were also used: JavaFX ‒ to create a user interface; SQLite JDBC 3.21.0 ‒ to work with the SQLite database; imgscalr ‒ to scale images; Apache Commons IO 2.6 to work with the file system; ControlsFX v8.40.14 ‒ to create a user interface.Results. The developed software product based on fractal methods makes it possible to significantly highlight the textural features of images, on the basis of which the clustering operation of selected objects of interest in images is performed in order to export them for further classification.Conclusion. During the implementation of the project, a software product for visualization of the Mandelbrot set was implemented, which can be used to model objects having a fractal shape, in relation to the processing of complexly structured images containing invisible hidden features of objects in the images.

Public Art Design Practice under Visual Communication Design

Abstract The expansion of visual communication design in public art makes the scope of visual communication wide. This new art form reflects the cross and integration of disciplines but also makes the form of public art in our life richer, and people can get more beautiful enjoyment. Research on the fractal algorithm in the escape time algorithm studied the Julia set in different function conditions of the fractal graph of the change and the function of different indices of the joint. The fractal graph obtained a colorful, more tense structure. Subsequently, it is applied to public art design, and after testing its performance, the fractal design of visual communication is combined with the IPA model to explore the practical effect of the fractal design in public art design. The results show that the improved fractal algorithm proposed in this paper increases the pattern generation rate from 61.5% to 92.6%. The fractal dimension measurement of 15 typical batik patterns shows that more than 85% of the batik patterns have an average value of more than 15000.

Fractal Few-Shot Learning.

Forming deep feature embeddings is an effective method for few-shot learning (FSL). However, in the case of insufficient samples, overcoming the task complexity while improving the accuracy is still a major challenge. To address this problem, this article considers the consistency between similar data from the fractal perspective, introduces a priori knowledge, and proposes a fractal embedding model by combining FSL with fractal dimension theory for the first time. We improve the original fractal dimension algorithm used to describe image texture roughness to suit a neural network. Moreover, in accordance with the improved algorithm, prior knowledge of the quantized image is integrated into the features to reduce the impact of the data distribution on the model. Experimental results obtained on multiple image benchmark datasets show that the performance of the proposed model exceeds or matches that of previous state-of-the-art models. In addition, the proposed model achieves the best performance in cross-domain scenarios, further illustrating its robustness.

Characterization and Identification of Cracks on Perforated Embryo Eggs Based on Fractal Theory

Highlights A fractal matrix model was established to characterize the cracks on the surfaces of perforated embryo eggs. A function for classifying perforated embryo eggs was constructed using the Fisher linear discriminant algorithm. An experiment to identify the qualification of perforated embryo eggs was performed. Abstract. In response to the problems of low accuracy and unsatisfactory consistency in manual identification, a method for characterizing and identifying cracks on perforated embryo eggs is proposed based on fractal theory. Due to the intersection of the fractal dimensions of a few qualified and cracked embryo eggs, an improved fractal box-counting algorithm was used to characterize the overall characteristics of the cracks and construct an 8 × 8 fractal matrix using image segmentation technology. Based on the morphology and structure, the eggshell was divided into three regions and five characteristic variables expressing perforation cracks were extracted. Two significant variables were screened using the stepwise method to construct a linear discriminant function. Ten-day-old embryonated eggs of white phoexix black-bone chickens were selected as experimental materials. Embryo egg perforation and image acquisition devices were established. Then, crack recognition experiments were carried out. The accuracy of crack determination was 98.89%, and the identification time for a single egg was less than 1.24 s. The research results can lay a solid theoretical and practical foundation for the development of automatic recognition systems for perforated embryo eggs. Keywords: Characterization analysis, Crack, Fractal theory, Image processing, Linear discrimination.

Linear Fractals with Weights

Linear fractals associated with weights are investigated. Such fractals are important from a conservation law perspective that is relevant in a variety of physical systems such as materials science, sand dune fractals, barred galaxies, as well as in temporal processes like in the electroencephalogram (EEG). The weight associated with fractals is an additional feature that may be associated with distributions consistent with the ubiquitous power law and the first digit phenomenon. These distributions form a bridge to processes and applications in natural, biological, and engineering systems and, therefore, open up the possibility of the application of linear weighted fractals to these subjects. Two linear fractal algorithms that are near optimal in the information theoretic sense are described. A mechanism for the emergence of these fractals is proposed: it is the indistinguishability amongst the particles in the evolution and transformation of physical systems. Since the fractal approach is an established method of signal processing and coding, the newly proposed weighted fractals have the potential to lead to new useful algorithms.

Improved Steganography for IoT Network Node Data Security Promoting Secure Data Transmission using Generative Adversarial Networks

An internet of things (IoT) is an intelligent environment such as homes and smart cities of our country, and IoT improves the new technology implementation for home automation. The problem with security in IoT-based devices is that data transmission and signal passing are easily hacked using encryption and decryption methods. The old technology of the Steganography method does not improve the data hidden in images because encryption and decryption use a 1-bit 0.05-bit store, and low ranges hide the information in images, so that information hides out of the size and bits of the image. The hackers easily hack the hide information pixel by pixel or bit by bit in images. So, need for a proposed system, new technology, or methods. The suggested solution improves data concealment in photos by combining CNN’s deep learning techniques with steganography. The secret information these photographs convey can be shared without drawing hackers’ notice. The data is encrypted before being embedded in the image to increase its security. Steganography messages are frequently encrypted using more conventional methods first, after which the encrypted message is added to the cover image in some manner. The previous algorithm of SFNET algorithm architecture has been divided by segment, the segment based on width, height, and depth changes based improve performances. Existing systems of SFNET and SRNET are compared to the fractal net algorithm to improve the performance of 3 to 1 % of the proposed system.

Adaptive stochastic fractal search algorithm for multi-objective optimization

Stochastic fractal search algorithm, a relatively efficient algorithm has certain advantages in solving multi-objective optimization problems. Decomposition-based strategy is effective for solving multi-objective optimization, which guarantees the diversity of solutions. On the other hand, a challenge for decomposition-based strategy is to enhance the algorithm’s convergence while maintaining the algorithm’s distribution. This paper proposes a reference vector-guided stochastic fractal search algorithm for multi-objective optimization(RVSFS). In the proposed algorithm, the leader solution of each subspace is selected by reference vectors to assist the generation of new solutions and ensure the convergence of the algorithm. A new selection criterion length–angle distance (LAD) is proposed. Furthermore, the Gaussian walk and Levy flight are conducted in different searching stages to balance the exploration and exploitation ability. To speed up convergence and maintain the diversity of solutions, an adaptive dynamic proportion mechanism is designed when using the random fractals and Gaussian walks to generate offspring. Since information is shared and exchanged among different solutions in each iteration, the searching process is accelerated and the exploration capability can be enhanced contemporary. On top of this, a vector-guided enhanced selection operator is designed in the elite selection step to provide desirable distribution. Our experimental results on 45 benchmarks from UF and WFG test suits show prominent competitiveness compared with five state-of-the-art algorithms. RVSFS is very competitive on all 9 UF benchmarks in terms of the metric inverted generational distance and also performs well on 14 of 36 benchmarks from WFG in terms of the metric inverted generational distance and the metric hypervolume.